Generally speaking, a father cannot get out of, or reduce, his child support obligation by just quitting a good paying job and moving to a place where he has no job or a lesser paying job. Sometimes it might be allowed if the overall plan serves the best interests of the children over the long term. That doesn't seem to be the situation in your case.
There is a provision in Florida law that allows you to seek an injunction, seize his property or accounts, require him to post a bond, or to secure any other order that might be necessary to secure the continuation of his child support payments if he is about to remove himself or his property out of state. This is an area of the law where you would be best served by consulting in more depth with an attorney.
Answered on Nov 25th, 2013 at 7:29 PM